球形拓扑晶体中的位错屏蔽
Dislocation screening in crystals with spherical topology
摘要：
尽管向错缺陷在二维平面晶体中是能量上禁止的，但它们的存在在具有球形拓扑结构的晶体中是必要的，例如病毒衣壳、胶体体或富勒烯。这样的几何挫折引起大的弹性应力，当其尺寸显著大于典型的晶格间距时，这使得晶体不稳定。根据晶体对拉伸和弯曲变形的顺应性，这些应力通过向错附近的固有曲率的局部增加或通过过量位错的增殖来减轻，过量位错通常以称为“疤痕”的一维链的形式组织。疤痕的相关应变场可以抵消孤立的向错所产生的应变场。本文发展了亏格为1的二维闭合晶体中位错屏蔽的连续介质理论。通过将给定向错产生的疤痕通量建模为独立的标量场，我们证明了具有不同非球面度的封闭二维晶体的弹性能可以表示为零温度和有限温度下向错屏蔽拓扑电荷的简单二次函数。这使我们能够预测多余位错的最佳密度以及晶体获得的最小拉伸能量。
英文摘要：
Whereas disclination defects are energetically prohibitive in two-dimensional flat crystals, their existence is necessary in crystals with spherical topology, such as viral capsids, colloidosomes or fullerenes. Such a geometrical frustration gives rise to large elastic stresses, which render the crystal unstable when its size is significantly larger than the typical lattice spacing. Depending on the compliance of the crystal with respect to stretching and bending deformations, these stresses are alleviated by either a local increase of the intrinsic curvature in proximity of the disclinations or by the proliferation of excess dislocations, often organized in the form of one-dimensional chains known as "scars". The associated strain field of the scars is such to counterbalance the one resulting from the isolated disclinations. Here, we develop a continuum theory of dislocation screening in two-dimensional closed crystals with genus one. Upon modeling the flux of scars emanating from a given disclination as an independent scalar field, we demonstrate that the elastic energy of closed two-dimensional crystals with various degrees of asphericity can be expressed as a simple quadratic function of the screened topological charge of the disclinations, both at zero and finite temperature. This allows us to predict the optimal density of the excess dislocations as well as the minimal stretching energy attained by the crystal.
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